The question asks if lines $L_1$ and $L_2$ in the graph are parallel, based on their slopes.

Explanation:

To determine if two lines are parallel, we need to compare their slopes. Two lines are parallel if and only if they have the same slope.

Finding the slope of $L_1$:

From the graph, the points on $L_1$ are $(0, -5)$ and $(8, -2)$. The slope of a line can be found using the formula:

$\text{slope of } L_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - (-5)}{8 - 0} = \frac{-2 + 5}{8} = \frac{3}{8}$

Finding the slope of $L_2$:

The points on $L_2$ are $(0, 1)$ and $(-6, 2)$. Applying the slope formula again:

$\text{slope of } L_2 = \frac{2 - 1}{-6 - 0} = \frac{1}{-6} = -\frac{1}{6}$

Conclusion:

The slopes of $L_1$ and $L_2$ are $\frac{3}{8}$ and $-\frac{1}{6}$, respectively. Since these slopes are not equal, the lines are not parallel.

Thus, the correct answer is A: No, lines $L_1$ and $L_2$ are not parallel because they have different slopes.

Would you like more details or further explanations?

Related Questions:

1. What happens if two lines have the same slope but different y-intercepts?
2. How can you determine if two lines are perpendicular based on their slopes?
3. What is the significance of the negative sign in a slope?
4. How can you find the slope of a line from an equation rather than points?
5. How can parallel lines be useful in geometric proofs?

Tip:

Always check for sign errors when calculating slopes, especially when subtracting negative numbers!